Properties

Level $8$
Weight $0$
Character 8.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 13.5881834525 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.655742087\) \(a_{4}=+0.000000000\) \(a_{5}=+0.129456323\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.365026430\) \(a_{8}=+0.000000000\) \(a_{9}=+1.741481860\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.362256503\) \(a_{12}=+0.000000000\) \(a_{13}=+1.932932407\) \(a_{14}=+0.000000000\) \(a_{15}=+0.214346282\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.407765450\) \(a_{18}=+0.000000000\) \(a_{19}=+0.411563171\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.260131711\) \(a_{22}=+0.000000000\) \(a_{23}=+0.862887909\) \(a_{24}=+0.000000000\) \(a_{25}=-0.983241061\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.227702723\) \(a_{28}=+0.000000000\) \(a_{29}=+1.502249003\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.785628638\) \(a_{32}=+0.000000000\) \(a_{33}=+0.599803336\) \(a_{34}=+0.000000000\) \(a_{35}=-0.176711295\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.997916903\) \(a_{38}=+0.000000000\) \(a_{39}=+3.200437673\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.063728417\) \(a_{42}=+0.000000000\) \(a_{43}=-0.454396890\) \(a_{44}=+0.000000000\) \(a_{45}=+0.225443957\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.282663302\) \(a_{48}=+0.000000000\) \(a_{49}=+0.863274105\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.675206222\) \(a_{52}=+0.000000000\) \(a_{53}=-0.488814502\) \(a_{54}=+0.000000000\) \(a_{55}=+0.047657765\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.679070413\) \(a_{58}=+0.000000000\) \(a_{59}=-0.568348485\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.073929369\) \(a_{62}=+0.000000000\) \(a_{63}=-2.358132288\) \(a_{64}=+0.000000000\) \(a_{65}=+0.000446703\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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